JAMES CLEWETT: Today's video is
going to be all about the National Lottery. And if you're a number freak
like me, then the National Lottery is great because it's
that two times a week when all the people at home get
to share in my enthusiasm for numbers. So what I want to do today is
talk a little bit about some of the probabilities involved
in the National lottery. So before we start, I think we
should choose some numbers for our lottery. So our first number is going
to be the number 14. That's my birthday. Then I think we'll have
the number 19. That was a nice, good year
for me, 19 years old. We'll have a few in the 30s-- 31, and 33, and 34. OK, and then one more, 45. So I've chosen the number 14
for my birthday, the number 19, and then, a few in the 30s,
number 31, 33, and 34, and number 45. So now, what are the odds of
us picking those same six balls out of our homemade
lottery kit? First of all, to start with,
there are six balls in here which are winners for us. And there are 49 balls
just like the national lottery game. OK, so I'm going to look away. And I'm going to select. And it's number 19,
a 6 out of 49. OK, so we put that
one to one side. But now they're only 48 balls
left in the basket. And we've got five winners
left in the box. OK, let me give that
a good stir around. And it's the number 45. Put that one to one side, and
again, now, we've got one less ball in the box. So we're down to 47 balls and
just four winners now. Give them a good stir. It's the number 31. And that one, again, goes to
one side with our other winning balls. Just 46 balls left in here
now, and only 3 winners. There it is. The number 14. OK, again, put that
one on one side. Give ourselves a little stir. Now there's only 45 balls left
and just two winners. There it is. The number 33. OK, so we've got one winning
ball left in the bucket. So give it a stir. There it is. The number 34. OK, so my chances of picking out
the number 34, were just 1 from 44 balls. And there we have it. What were the odds of me
winning the lottery and retiring to become a part-time
physicist? Well, let's have a look at it. The chance of getting the first
number was 6 in 49. Then it's a completely
independent event, so we can just multiply that by the chance
of getting the second number, which is 5 in 48. So I can just just
multiply that. Then we multiply that
by the chance of winning the third number-- the top line we can
do in our head-- is simply 720. The bottom line-- I'm going to cheat-- I'm going to use a calculator. 49 times by 48 times by
47 times by 46 times by 45 times by 44. And that's the number 10
billion and change. So we're going to write down
our 10 billion here. So that gives us our final
answer in math speak, if you like, of 7.151 times
10 to the minus 8. That number doesn't really mean
anything to most of us. And so I'm going to write
this as 1 over 13983816. So the odds of winning the
lottery are one part in 13,983,816. Or in real money, about one
part in 14 million. I play the lottery
at Christmas. Actually, I find it's been
really good fun. So I tend to spend
about a fiver a year on lottery numbers. And for that one week that
I've bought a ticket, I daydream about all the really
cool things that I'm going to do if I win the lottery. So how much is that worth? I don't know. I really enjoy it. I really enjoy just
the process of owning a lottery ticket. But I know-- I'm reasonably numerically
grounded-- I know that my chances
of winning are very, very close to zero. I think my chances of being
struck by lightning are something like seven times
higher than my chances of winning the lottery. So I'm kind of hoping
that doesn't happen. So we've won the lottery. We've matched six balls. That's absolutely fantastic. But it doesn't really explain
why every time I've bought a lottery ticket, I've not matched
any balls at all. So what's the probability of
buying a lottery ticket and matching no balls? So let's go back to the numbers
that we selected. So we had 14-- OK, so this were our
magic numbers. So what are the odds of
selecting a first number which doesn't match? Well, there are 43 balls
in there, out of 49 which don't match. So I'm going to select one. It's number 38. OK, so that doesn't match. I don't want that one. Give it a stir. Now remember, here we go. That's the number 35. And, again, it doesn't match. Give them a stir. It's the number 25. Again, no use to me. 41 out of 47. OK, so the next one. Number 23. Getting a little annoyed
with this. That's no good to me either. So the chance of pulling
out a nonwinner there were 40 out of 46. OK. Do another one. I've got the number 41. No use. OK. So the chances, again-- 39 out of 45. And our last ball-- BRADY HARAN: Hang on, what do
you think it's going to be? JAMES CLEWETT: Well,
I don't think it's going to be a winner. That's for sure. Uh, give it a stir. I hope it's not a winner. Number 43. OK, so we've got no
balls at all. Rubbish. Right. The chances of a nonmatch-- 38 out of 44. If we calculate this number
through-- again I'm going to turn to my calculator. OK? So our probability of picking
no matches whatsoever is 4 billion divided by 10
billion, which is-- sorry-- 43%, 43.59649%. Somebody is spending a pound
a week playing the lottery. And for that pound a week,
they're getting hope and excitement and a Saturday
night buzz. I think that's great
value to be honest. So that's fine. But if I hear of somebody who's
spending 10, 20 quid a week buying lottery
tickets, stop. Please stop.
